Nonequilibrium Steady-State Transport in Quantum Impurity Models: a Thermofield and Quantum Quench Approach using Matrix Product States

TL;DR

This paper introduces a combined thermofield and quantum quench approach with matrix product states to accurately study nonequilibrium steady-state transport in quantum impurity models, overcoming limitations of traditional methods.

Contribution

It develops a novel method integrating thermofield and quench techniques with MPS to reliably analyze nonequilibrium impurity transport at low energies.

Findings

Achieves <3% error in current calculations at low energies.

Provides benchmark results for temperature and magnetic field dependence.

Demonstrates effectiveness for the single-impurity Anderson model.

Abstract

The numerical renormalization group (NRG) is tailored to describe interacting impurity models in equilibrium, but faces limitations for steady-state nonequilibrium, arising, e.g., due to an applied bias voltage. We show that these limitations can be overcome by describing the thermal leads using a thermofield approach, integrating out high energy modes using NRG, and then treating the nonequilibrium dynamics at low energies using a quench protocol, implemented using the time-dependent density matrix renormalization group (tDMRG). This yields quantitatively reliable results for the current (with errors $\lesssim 3\%$) down to the exponentially small energy scales characteristic of impurity models. We present results of benchmark quality for the temperature and magnetic field dependence of the zero-bias conductance peak for the single-impurity Anderson model.